基于快速广义反射透射系数方法的面波群速度计算
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摘要
在利用实际地震资料反演地球内部结构时,群速度往往比相速度更有意义.本文在水平层状均匀介质模型中,用快速广义反射透射系数方法(Pei,2008)计算了基阶瑞雷面波的群速度,并推导了Chen(1993)4×4层矩阵E的逆的解析表达式.文中用数值实验的方法合成了两个典型模型的群速度频散曲线,并与复合矩阵方法计算的结果进行了对比,结果表明本文的方法是切实可行的,与广义反射透射系数方法相比明显地提高了计算效率,尤其是在高频、层厚度大和层数多的情况下表现得变为突出.
Group velocities of surface waves are more significative than phase velocities when we inverse the structure of the earth's interior by seismic data.In this study we calculate the group velocity of Rayleigh waves based on the Fast Generalized R/T coefficient Method (FGRT)developed by Pei (2008),for the homogeneous horizontal multilayered model and present an analytic solution for the inverse of the 4 × 4 layer matrix E in the traditional generalized R/T coefficient method of Chen(1993).Dispersion curves of two typical models are computed by numerical experiments,whose results are compared with the compound matrix method.It demonstrates that our method is feasible.Compared with the Generalized R/T coefficient method(Chen 1993),our research enhances the calculation efficiency greatly,especially in the cases of the high-frequency,thicker layers and more layers conditions.
Group velocities of surface waves are more significative than phase velocities when we inverse the structure of the earth's interior by seismic data.In this study we calculate the group velocity of Rayleigh waves based on the Fast Generalized R/T coefficient Method (FGRT)developed by Pei (2008),for the homogeneous horizontal multilayered model and present an analytic solution for the inverse of the 4 × 4 layer matrix E in the traditional generalized R/T coefficient method of Chen(1993).Dispersion curves of two typical models are computed by numerical experiments,whose results are compared with the compound matrix method.It demonstrates that our method is feasible.Compared with the Generalized R/T coefficient method(Chen 1993),our research enhances the calculation efficiency greatly,especially in the cases of the high-frequency,thicker layers and more layers conditions.
引文
[1] Haskell N A.The dispersion of surface waves on multi layered media[J].Bull.Seism.Soc.Am.,1953,43:17～34．
[2] Pestel E,Leckie F A.Matrix methods in elasto-mechanics[M].New York:McGraw-Hill,1963．
[3] Thrower E N.The computation of the dispersion of elastic waves in layered media[J].J.Sound.Vibr.,1965,2:210～226．
[4] Dukin J W.Computation of modal solutions in layered,elastic media at high frequencies[J].Bull.Seism.Soc.Am.,1965,53(2) :335～358．
[5] Watson T H.A note on fast computation of Rayleigh wave dispersion in the multi-layered elastic half space[J].Bull.Seism.Soc.Am.,1970,60:161～166．
[6] Buchen P W,Ben Hador R.Free mode surface-wave computations[J].Geophys.J.Int.,1996,124:869～ 887．
[7] Knopoff L.A matrix method for elastic wave problems[J].Bull.Seism.Soc.Am.,1964,54:431～438．
[8] Schwab F.Surface wave dispersion computations:Knopoff's method[J].Bull.Seism.Soc.Am.,1970,60:1491～1520．
[9] Abo Zena A M.Dispersion function computations for unlimited frequency values[J].Geophys.J.R.Astr.Soc.,1979,58:91～105．
[10] Kennett B L N.Reflection,rays and reverberations[J].Bull.Seism.Soc.Am.,1974,64:1685～1696．
[11] Kennett B L N,Kerry N J.Seismic waves in a stratified halfspace[J].Geophys.J.R.Astr.Soc.,1979,57:557～583．
[12] Kennett B L N,Kerry N J.Seismic waves in a stratified half space Stratified Media[M].Cambridge U Press.1979,57:557 ～583．
[13] Kerry N J.Synthesis of seismic surface wave[J].Geophys. J.R.Astr.Soc.,1981,64:425～446．
[14] Kennett B L N.Seismic waves in a stratified half-space-Ⅱ.Theoretical seismograms[J].Geophys.J.R.Astr.Soc.,1980,61:1～10．
[15] Kennett B L N.Seismic Wave Propagation in Stratified Media[M].NewYork:CamhridgeU Press,1983．
[16] LucoJ E,Apsel RJ.On the Green's function fora layered half-space[J].Part Ⅰ.Bull.Seism.Soc.Am.,1983,73:909～929．
[17] Chen X F.A systematic and efficient method of computing normal modes for multi-layered half space[J].Geophys.J.Int.,1993,115:391～409．
[18] 何耀锋,陈蔚天,陈晓非.利用广义反射-透射系数方法求解含低速层水平层状介质模型中面波频散曲线问题[J].地球物理学报,2006,49(4) :1074～1081． He Y F,Chen W T,Chen X F.Normal mode computation by the generalized reflection-transmission coeffieient method in planar layered half space[J].Chinese J.Geophys.(in Chinese),2006,49(4) :1074～1081．
[19] Pei D H,John N L,etal.Improvements on computation of phase velocities of rayleigh waves based on the generalized r/ t coefficient method[J].Bull.Seism.Soc.Am.,2008,98 (1) :280～287．
[20] Aki K,Richards P G..Quantitative seismology:theory and methods[M].San Francisco:W.H.Freeman,1980．
[21] 凡友华,陈晓非,刘雪峰,等.Rayleigh波的频散方程高频近似分解和多模式激发数目[J].地球物理学报,2007,50(1) : 233～239． Fan Y H,Chen X F,Liu X F,et al.Approximate decomposition of the dispersion equation at high frequencies and the number of multimodes for Rayleigh waves[J].ChineseJ.Geophys.(in Chinese),2007,50(1) :233～239．
[2] Pestel E,Leckie F A.Matrix methods in elasto-mechanics[M].New York:McGraw-Hill,1963．
[3] Thrower E N.The computation of the dispersion of elastic waves in layered media[J].J.Sound.Vibr.,1965,2:210～226．
[4] Dukin J W.Computation of modal solutions in layered,elastic media at high frequencies[J].Bull.Seism.Soc.Am.,1965,53(2) :335～358．
[5] Watson T H.A note on fast computation of Rayleigh wave dispersion in the multi-layered elastic half space[J].Bull.Seism.Soc.Am.,1970,60:161～166．
[6] Buchen P W,Ben Hador R.Free mode surface-wave computations[J].Geophys.J.Int.,1996,124:869～ 887．
[7] Knopoff L.A matrix method for elastic wave problems[J].Bull.Seism.Soc.Am.,1964,54:431～438．
[8] Schwab F.Surface wave dispersion computations:Knopoff's method[J].Bull.Seism.Soc.Am.,1970,60:1491～1520．
[9] Abo Zena A M.Dispersion function computations for unlimited frequency values[J].Geophys.J.R.Astr.Soc.,1979,58:91～105．
[10] Kennett B L N.Reflection,rays and reverberations[J].Bull.Seism.Soc.Am.,1974,64:1685～1696．
[11] Kennett B L N,Kerry N J.Seismic waves in a stratified halfspace[J].Geophys.J.R.Astr.Soc.,1979,57:557～583．
[12] Kennett B L N,Kerry N J.Seismic waves in a stratified half space Stratified Media[M].Cambridge U Press.1979,57:557 ～583．
[13] Kerry N J.Synthesis of seismic surface wave[J].Geophys. J.R.Astr.Soc.,1981,64:425～446．
[14] Kennett B L N.Seismic waves in a stratified half-space-Ⅱ.Theoretical seismograms[J].Geophys.J.R.Astr.Soc.,1980,61:1～10．
[15] Kennett B L N.Seismic Wave Propagation in Stratified Media[M].NewYork:CamhridgeU Press,1983．
[16] LucoJ E,Apsel RJ.On the Green's function fora layered half-space[J].Part Ⅰ.Bull.Seism.Soc.Am.,1983,73:909～929．
[17] Chen X F.A systematic and efficient method of computing normal modes for multi-layered half space[J].Geophys.J.Int.,1993,115:391～409．
[18] 何耀锋,陈蔚天,陈晓非.利用广义反射-透射系数方法求解含低速层水平层状介质模型中面波频散曲线问题[J].地球物理学报,2006,49(4) :1074～1081． He Y F,Chen W T,Chen X F.Normal mode computation by the generalized reflection-transmission coeffieient method in planar layered half space[J].Chinese J.Geophys.(in Chinese),2006,49(4) :1074～1081．
[19] Pei D H,John N L,etal.Improvements on computation of phase velocities of rayleigh waves based on the generalized r/ t coefficient method[J].Bull.Seism.Soc.Am.,2008,98 (1) :280～287．
[20] Aki K,Richards P G..Quantitative seismology:theory and methods[M].San Francisco:W.H.Freeman,1980．
[21] 凡友华,陈晓非,刘雪峰,等.Rayleigh波的频散方程高频近似分解和多模式激发数目[J].地球物理学报,2007,50(1) : 233～239． Fan Y H,Chen X F,Liu X F,et al.Approximate decomposition of the dispersion equation at high frequencies and the number of multimodes for Rayleigh waves[J].ChineseJ.Geophys.(in Chinese),2007,50(1) :233～239．
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